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ABRIDGED 



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INTEREST TABLES, 



-BY- 



M. L. EDMUNDS. 



i 



Reporter Print, McMiaEvilie, Or, J^ 



ABRIDGED 



INTEREST TABLES, 



rf^ 



-BY- 




M. L. EDMUNDS. 



Reporter Print, McMirmville, Or, 






HFvi.fr 






Entered according to act of Congress, in the year 188G, by 

MILTON L. EDMUNDS, 
In the office of the Librarian of Congress, at Washington. 



o 



INTRODUCTION, 



The importance of a method that can be read- 
ily applied in the calculation of interest, lias led 
to the exercise of considerable ingenuity in or- 
der to discover the shortest and simplest rule in 
practice. The object of this work, which gives the 
method used by the author in the preparation of 
his Complete Interest Tables, is to present a 
method for computing interest, not only brief, 
but one that will give correct interest; this be- 
ing a feature in which most brief methods are 
deficient in consequence of reckoning time incor- 
rectly. It may be readily seen that an error 
arises in the use of all methods for com- 
puting interest, whereby the year is reck- 
oned at 360 days, or what is equivalent, at 12 
months of 30 days each. Such objection applies 
to the 6 per cent, method, also to various other 
methods which by reckoning 380 days to the year, 
give, for fractional parts of a year, an excess of 
interest equal to one seventy-third of the entire 
interest. 



4 INTRODUCTION. 

There being 365 days in a year, it is impossi- 
ble to divide the year into months each contain- 
ing an equal number of entire days; hence the 
impracticability of reckoning time in months. 
This difficulty may be obviated by using methods 
whereby interest is calculated for the number of 
days. The only correct methods are thDse by 
which interest, for periods of time less than one 
year, is calculated for the exact number of days, 
and the most practical method is that which by 
the most natural process, with the least amount 
of labor, will give exact interest. 

Exact interest, obtained by reckoning 365 days 
to the year, is growing in favor with bankers and 
other business men, is the method of interest 
used by the United States Government, and by 
foreign correspondents, and is the method of in- 
terest becoming the most popular and the most 
commonly used. 

In solving problems in simple interest, the 
primary object is to find the interest on a given 
principal for a given time and rate. That process 
which is the most natural and which is the most 
simple in principle, is to find the interest for 
one year by multiplying the principal by the 
rate, and multiplying this interest by the 
time in years. The objection to this method, 



INTRODUCTION. 5 

heretofore, has been in the difficulty of multiply- 
ing by the time, which given in months and days, 
has been considered incapable of being reduced 
to convenient fractional parts of a year. The 
method by abbreviated multiplication of deci- 
mals, presented in this work, enables us to follow 
the natural process, while at the same time it 
gives us the shortest method possible for calculat- 
ing exact interest. 

The subject may be conveniently treated under 
three cases, viz: to find the time; to express the 
time in years ; aqxl, to find the required interest. 
To this is appended a general rule together with 
a variety of problems illustrating the method of 
obtaining, and multiplying by, the decimal years. 

The amount of table work, not aggregating 
one-half page, all of which should be carefully 
committed to memory, forms a characteristic fea- 
ture of this method; there being so little required 
to be memorized in order to compute time readily 
or to reduce days to decimal years. It should also 
be observed that if the periods of time, 30, 60, 
and 90 days, so frequently used, have their re- 
spective decimal years memorized, the computa- 
tion of interest for these periods becomes suscepti- 



6 INTRODUCTION. 

ble of easy mental calculation. When grace is 
allowed, calculate for the additional legal number 
of days. 

It is not within the author's province to 
present a treatise on the fundamental rules of 
arithmetic ; therefore, those who are desirous of 
perfecting themselves in the method for comput- 
ing interest, given in this work, should first be- 
come familiar with the fundamental operations, 
also with decimals and with circulates, subjects 
treated exhaustively in all higher arithmetics. 

Having prosecuted the work with the view of 
facilitating the calculation of interest, the author 
now submits his method to the candor and dis- 
cernment of those whose avocations demand a 
practical treatise on this important subject, and 
leaves whatever merit the method deserves to the 
decision of those competent to judge. 

M. L. Edmunds. 



ABRIDGED INTEREST TABLES. 



TO FIND THE TIME. 

The following table which gives the number 
of days in the year previous to the first day of 
each month, should be thoroughly committed to 
memory. 

January May 120 September . 243 

February 31 June 151 October. . . . 273 

March 59 July 181 November.. . 304 

April .90 August. ... 212 December .. 334 

To find the day of the year of any date, add 
the day of the month to the number in the table 
corresponding to the month, the sum will give the 
day of the year. Example: The number in the 
table corresponding to March is 59, which is the 
number of days in the year previous to March 
1st. The day of the year corresponding to March 
10th is found by taking the sum of 59 and 10 
which is 69. Hence March 10th is found to be 
the 69th day of the year. 

To find the difference of time between two dates, 
subtract the day of the year of the former date 
from the day of the year of the latter date, the 



8 ABRIDGED INTEREST TABLES. 

remainder will be equal to the difference of time 
in days between the two dates. Example : By 
the table, February 12th is found to be the 43d 
day of the year, and July 20th, the 201st day of 
the year. The difference of time in days from 
February 12th to July 20th is found by taking 
the difference between 43 and 201 which is 158. 

If the dates are in successive years, and the 
time less than one year, subtract the day of the 
year of the former date from 365 and add the re- 
mainder to the day of the year of the latter date. 
Example : November 15th is the 319th day of 
the year. The number of days from November 
15th to the close of the year is equal to the differ- 
ence between 319 and 365 which is 46. February 
10th, is the 41st day of the year. Hence, the 
number of days from November 15th to Febru- 
ary 10th is equal to the sum of 46 and 41, which 
is 87. 

If the time exceeds one year, determine the 
number of entire years, and then reckon the ex- 
act number of days remaining. 

In passing over February in leap year, add 
1 to the number of days found by the table. 



ABRIDGED INTEREST TABLES. 9 

TO EXPRESS THE TIME IN YEARS. 

Since 1 day is ^ of a year, any number of 
days will equal the same number of 365ths of a 
year, and the common fraction thus formed may 
be reduced to a decimal fraction by annexing ciph- 
ers to the numerator of the fraction and dividing 
by the denominator. Example: Ninety three days 
equals ^ of a year, and this fraction reduced to 
decimal years equals .254794520 years. 

The decimal .254794520, similar to all inter- 
minate decimals obtained by reducing any num- 
ber of 365ths, is a mixed circulate containing the 
complementary repetend 54794520, which will 
continue to repeat however far the decimal may 
be expanded. 

In reducing the common fraction to a decimal, 
it is unnecessary to continue the division further 
than is required to obtain the first half of the 
repetend, since the last half may be found by 
subtracting the terms of the first half respectively 
from 9. The entire repetend being found, the 
decimal may be expanded indefinitely by repeat- 
ing the terms of the repetend. Observe that the rep- 
etend should begin with the second figure of the de- 

90 

cimal. Example: 90 days equals ^ of a year. An- 



10 ABRIDGED INTEREST TABLES. 

nexing ciphers to the numerator of the fraction 
and dividing by the denominator, continuing the 
division five decimal places, gives .24657, and we 
have 2, the finite portion of the decimal, and 
4657, the first half of .the repetend. Subtracting 
the terms of the first half of the repetend re- 
spectively from 9, to obtain the terms of the last 
half, we have the mixed circulate .246575342, 
which may be expanded indefinitely by repeating 
the terms of the repetend; thus, .246575342465 etc. 
When the number of days is a multiple of 5 the 
repetend w r ill begin with the first figure of the 
decimal ; but to preserve uniformity in practice, 

regard the second figure of the decimal as the 
first figure of the repetend. 

As the number of decimal places ordinarily 
required is from three to five, the above principle 
of circulates is employed to expedite the process 
of reduction only when interest is required on 
extremely large amounts. 

In every instance the reduction may be much 
more rapidly performed if the following table be 
committed to memory. 

365x1=365 365x4=1460 365x7=2555 
365x2= 730 365x5=1825 365x8=2020 
365x3=1005 365x6=2100 365x0 = 3285 



ABRIDGED INTEREST TABLES. 11 

TO FIND THE INTEREST. 

Example: Required the interest of $3,987, for 
5 years and 316 days, at 5 per cent. 

The time expressed decimally equals 5.86575-1- 
years. 

OPERATION. 

$3987=Principal. 
.05=Rate. 



199.35=Interest for 1 year. 
57568. 5=Time expressed decimally. 



996.75=Interest for 5 years. 
159.48=Interest for 8 tenths of a year. 
11.96=Interest for 6 hundredths of a year. 
1.00=Interest for 5 thousandths of a year. 
.14=lnterest for 7 ten-thousandths of a year. 
l=Interest for 5 hundred-thousandths of a year. 



$1169.34=Required interest. 

Multiplying the principal by the rate gives 
the interest for one year, and this interest multi- 
plied by the time in years gives the required in- 
terest. 

Since the interest is generally desired only in 
dollars and cents, the process of multiplying by 
the time in years expressed decimally, may be 
shortened by contracting each partial product to 
the desired denomination. 



12 ABRIDGED INTEREST TABLES. 

Multiplying the principal $3987 by the rate 
.05 gives $199.35 interest for 1 year, and this in- 
terest, divided by 10, 100, 1000, etc., will give 
$19.93-1-, $1.99-!-, $0.19-!-, etc., which equal 
the interest respectively for 1 tenth of a 
year, 1 hundredth of a year, 1 thousandth of 
a year, etc. By writing the terms of the decimal 
years,which are years, tenths of a year, hundredths 
of a year, thousandths of a year, etc., respectively 
under the right hand terms of the interest for 1 
year, 1 tenth of a year, 1 hundredth of a year, 1 
thousandth of a year, etc., we have the terms of 
the decimal years written in an inverted order, 
each properly written under the interest which 
must be multiplied by it. This arrangement en- 
ables us to contract each partial product to the re- 
quired denomination, and to reject all partial 
products of a lower denomination than required 
in the entire product. 

Multiply the interest for 1 year. 1 tenth of a 
year, 1 hundredth of a year, 1 thousandth of 
a year, etc., respectively, by the number of 
entire years, tenths of a year, hundredths 
of a year, thousandths of a year, etc., in- 
creasing each partial product by as many units as 



ABRIDGED INTEREST TABLES. 13 

would have been carried to it from the product of 
the rejected terms, and 1 more when the second 
term towards the right in the product of the re- 
jected terms is 5 or more than 5; and place the 
right hand terms of these partial products in the 
same column. The sum of these partial products 
will be the required interest. 

The rejected terms are the denominations 
lower than cents, in the interest for 1 year, 1 tenth 
of a year, 1 hundredth of a year, 1 thousandth of 
a year, etc. 

The terms of the decimal years must be ex- 
tended one place farther to the left than the num- 
ber expressing the interest for one year, in order 
to obtain the last partial product which is equal 
only to the number of units that would have 
been carried from the product of the rejected 
terms. 



14 ABRIDGED INTEREST TABLES. 

GENERAL RULE. 

1. Multiply the principal by the rate to find the inter- 
est for 1 year. 

2. Write the number of entire years which must not 
exceed 9, under that part of the interest for 1 year, gener- 
ally cents, which is of the lowest denomination required 
in the entire interest. If the time is less than 1 year, 
place a cipher for the first term of the decimal years. If 
the number of entire years exceeds 9, write for the first 
term of the decimal years, a column of figures whose sum 
equals the whole number of entire years. 

3. At the right of, and near to the number of years, 
write the number of days remaining, to which annex ci- 
phers and reduce to tenths of a year, hundredths of a year, 
thousandths of a year, etc., by dividing b} T 365 ; and write 
the number of tenths of a year, hundredths of a year, 
thousandths of a year, etc., in a reverse order at the left of 
the number of years, extending the terms of the decimal 
years, when interminate, one place farther to the left 
than the terms of the number expressing the interest for 
1 year. The divisor which is always 365, also the products 
of 365 by the quotient figures, may be written or unwrit- 
ten, according to ones familiarity with the process of re- 
duction. If the divisor is written, place it on the right of 
the number of days. 

4. Regard the interest for 1 year divided by 10, 100, 
1000, etc., which will give the interest respectively, for 1 
tenth of a year, 1 hundredth of a year, 1 thousandth of a 
year, etc. 

5. Multiply the interest for 1 year, 1 tenth of a year, 
1 hundredth of a year, 1 thousandth of a year, etc;., respect- 



ABRIDGED INTEREST TABLES. 15 

ively, by the number of entire years, tenths of a year, 
hundredths of a year, thousandths of a year, etc., increas- 
ing each partial product by as many units as would have 
been carried to it from the product of the rejected terms, 
and 1 more when the second term toward the right in the 
product of the rejected terms is 5 or more than 5 ; and 
place the right hand terms of these partial products in the 
same column. 

6. Add these partial products; the sum will be the 
required interest, 

EXACT INTEREST MAY ALSO BE RECKONED BY 
THE FOLLOWING RULE, 

Multiply the principal by the rate, and this product by 
the integral number of years; then multiply the interest 
for 1 year by the exact number of days remaining and 
divide by 365 ; and take the sum of the two results. 



16 



ABRIDGED INTEREST TABLES. 



EXAMPLES. 



EXAMPLE 1. 

Required the interest of 
$225, for 2 years and 40 days, 
at 8 per cent. 

OPERATION. 

$225. 
.08 



18.00 
5901.2 

36.00 

1.80 

16 

1 



40.0(365 
365 

3500 
3285 

2150 



$37.97 Ans. 

EXAMPLE 3. 

Required the interest 
$600, for 14 years and 
days, at 12 per cent. 

OPERATION. 

$600 
.12 



of 

22 



EXAMPLE 2. 

Required the interest of 
$256.75, for 93 days, at 5 
per cent. 

OPERATION. 

$256.75 
.05 



12.8375 
7452.0 

2.57 
.64 

5 
1 

' $3.27 Ans. 



93.0 
730 



2000 
1825 



1750 
1460 

2900 



72.00 
8 
2060.6 22.00 

1000 


$60.25 
.07 


4 2175 


576.00 

432.00 

4.32 

1 


2.5 


21.09 

.84 


$1012.33 Ans. 


$21.93 Ans 



EXAMPLE 4. 

Required the interest of 
$60.25, for 5 years and 73 
days, at 7 per cent. 

OPERATION. 



73.0 



4*>-*-<5t> 



LIBRARY OF CONGRESS 



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